We introduce ‘generalised higher-rank k-graphs’ as a class of categories equipped with a notion of size. They extend not only higher-rank k-graphs, but also the Levi categories introduced by the first author as a categorical setting for graphs of groups. We prove that examples of generalised higher-rank k-graphs can be constructed using Zappa–Szép products of groupoids and higher-rank graphs.

中文翻译：

---

高级图的概括

我们引入了“广义的高等级k图”作为配备大小概念的类别。它们不仅扩展了更高等级的k图，而且还扩展了第一作者引入的 Levi 类别，作为组图的分类设置。我们证明了广义高阶k图的示例可以使用群样和高阶图的 Zappa-Szép 积来构建。